   # We state that the ideal gas law tends to hold best at low pressures and high temperatures. Show how the van der Waals equation simplifies to the ideal gas law under these conditions. ### Chemistry: An Atoms First Approach

2nd Edition
Steven S. Zumdahl + 1 other
Publisher: Cengage Learning
ISBN: 9781305079243

#### Solutions

Chapter
Section ### Chemistry: An Atoms First Approach

2nd Edition
Steven S. Zumdahl + 1 other
Publisher: Cengage Learning
ISBN: 9781305079243
Chapter 8, Problem 160CP
Textbook Problem
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## We state that the ideal gas law tends to hold best at low pressures and high temperatures. Show how the van der Waals equation simplifies to the ideal gas law under these conditions.

Interpretation Introduction

Interpretation: How wander Waals equation simplifies to the ideal gas law under low pressure and high temperature should be explained.

Concept introduction:

By combining the three gaseous laws namely Boyle’s law, Charles’s law and Avogadro’s law a combined gaseous equation is obtained. This combined gaseous equation is called Ideal gas law.

According to ideal gas law,

PV=nRT

Where,

P = pressure in atmospheres

V= volumes in liters

n = number of moles

R =universal gas constant ( 0.08206Latm/Kmol )

T = temperature in kelvins

Ideal gas law tends to hold best at low pressure and high temperature

A modified ideal gas equation on account of molecular size and molecular interaction forces is termed as Van der Waals equation.

That is,                [P+a(nV)2](V-nb)=nRT

‘a’ and ‘b’ is called Van der Waals coefficient and are characteristic of the individual gas

•  a is a measure of intermolecular attraction
• b is a measure of size of the molecule

Where,

P = pressure in atmospheres

V= volumes in liters

n = number of moles

R =universal gas constant ( 0.08206L×atm/K×mol )

T = temperature in kelvins

### Explanation of Solution

Explanation

To explain: how wander Waals equation simplifies to the ideal gas law under low pressure and high temperature

Van der Waals equation is

[P+a(nV)2](V-nb)=nRT

Byexpandingtheequation,[P+an2V2]×(V-nb)=nRTPV+an2VV2-nbP-an3bV2=nRTPV+an2V-nbP-an3bV2=nRT

At low pressure and high temperature molar volume of gas will be high

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